Algorithmic enumeration of quaternionic lattices

atmire.migration.oldid2733
dc.contributor.advisorBauer, Mark
dc.contributor.advisorGreenberg, Matthew
dc.contributor.authorChisholm, Sarah
dc.date.accessioned2014-10-08T15:51:42Z
dc.date.available2014-11-17T08:00:53Z
dc.date.issued2014-10-08
dc.date.submitted2014en
dc.description.abstractIn this thesis, we develop and implement an algorithm in Magma for enumerating isometry classes of quaternionic lattices. This algorithm can be viewed as a higher rank generalization of that used for enumerating equivalence classes of left-ideals of quaternionic orders. Our key technical innovation is an adaptation of Kneserā€™s method of neighbours to the setting of quaternionic lattices. Central to this adaptation is the Morita equivalence between Hermitian spaces over the split quaternion algebra M2(F) and symplectic spaces over F.en_US
dc.identifier.citationChisholm, S. (2014). Algorithmic enumeration of quaternionic lattices (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/24766en_US
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/24766
dc.identifier.urihttp://hdl.handle.net/11023/1920
dc.language.isoeng
dc.publisher.facultyGraduate Studies
dc.publisher.institutionUniversity of Calgaryen
dc.publisher.placeCalgaryen
dc.rightsUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.
dc.subjectEducation--Mathematics
dc.subject.classificationNumber Thoeryen_US
dc.titleAlgorithmic enumeration of quaternionic lattices
dc.typedoctoral thesis
thesis.degree.disciplineMathematics and Statistics
thesis.degree.grantorUniversity of Calgary
thesis.degree.nameDoctor of Philosophy (PhD)
ucalgary.item.requestcopytrue
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